Regular grid subgraphs of maximal girth
General Mathematics
2022-09-07 v2
Abstract
The unit-distance graph on the -dimensional integer lattice is called the -dimensional grid. We attempt to maximize the girth of a -regular (possibly induced) subgraph of the -dimensional grid, and provide examples and bounds for selected values of and , along with more general results. A few cases involving alternative lattices are also considered.
Cite
@article{arxiv.2105.05797,
title = {Regular grid subgraphs of maximal girth},
author = {Jan Kristian Haugland},
journal= {arXiv preprint arXiv:2105.05797},
year = {2022}
}
Comments
13 pages. In Section 3, an infinite family of examples in 4 dimensions is given in this version. It covers the examples given in the first version. Some other very minor edits also in Section 3, and the paragraph about "spread" at the end of Section 1 is made a bit more clear and concise